Pythagoras' theorem

For learners

A right-angled triangle has one square corner. The longest side, opposite the square corner, is called the hypotenuse.

Draw a square on each side. The big square on the longest side has exactly the same area as the two smaller squares added together.

For the 3, 4, 5 triangle: 3 × 3 = 9 and 4 × 4 = 16. Add them: 25. And 5 × 5 = 25.

For grown-ups

Pythagoras' theorem says $a^2+b^2=c^2$, where $c$ is the longest side. To find a short side, rearrange: $a^2=c^2-b^2$.

Common mistakes

• Forgetting to take the square root at the end.
• Adding the squares when you need to subtract (finding a short side).
• Using it on a triangle that has no right angle.

Why it matters

It is used to find distances, to check corners are square in building, and in navigation and computer graphics.

Topics in quarter that use this

• Pythagoras' theorem
• Vectors
• Vectors in three dimensions

Read more

• Pythagorean theorem (Wikipedia)